Question

How do you factor `216x^3+1`?

Answer 1

`(6x+1)(36x^2-6x+1)`

Explanation:

This is a `color(blue)"sum of cubes"` which is factorised, in general, as

`color(red)(bar(ul(|color(white)(2/2)color(black)(a^3+b^3=(a+b)(a^2-ab+b^2))color(white)(2/2)|)))`

`216x^3+1=(6x)^3+1^3`

`rArra=6x" and " b=1`

`rArr216x^3+1=(6x+1)(36x^2-6x+1)`